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Ds-cdma chip waveform design for minimal interference under bandwidth, phase, and envelope constrain - Communications, IEEE Transactions on IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 11, NOVEMBER 1999
1737
DS-CDMA Chip Waveform Design
for Minimal Interference Under Bandwidth,
Phase, and Envelope Constraints
Mohamed A. Landolsi and Wayne E. Stark,
Fellow, IEEE
AbstractThis paper investigates the effect of chip waveform
shaping on the error performance, bandwidth connement, phase
continuity, and envelope uniformity in direct-sequence code-
division multiple-access communication systems employing offset
quadrature modulation formats. An optimal design methodol-
ogy is developed for the problem of minimizing the multiple-
access interference power under various desirable signal con-
straints, including limited 99% and 99.9% power bandwidth
occupancies, continuous signal phase, and near-constant enve-
lope. The methodology is based on the use of prolate sphe-
roidal wave functions to obtain a reduced-dimension discrete
constrained optimization problem formulation. Numerous design
examples are discussed to compare the performance achieved by
the optimally-designed chip waveforms with other conventional
schemes, such as offset quadrature phase-shift keying, minimum-
shift keying (MSK), sinusoidal frequency-shift keying (SFSK),
and time-domain raised-cosine pulses. In general, it is found that
while the optimized chip pulses achieved substantial gains when
no envelope constraints were imposed, these gains vanish when a
low envelope uctuation constraint was introduced. In particular,
it is also shown that MSK is quasi-optimal with regard to the
99% bandwidth measure, while the raised-cosine pulse is equally
good with both the 99% and 99.9% measures, but at the expense
of some envelope variation. On the other hand, SFSK is quasi-
optimal with regard to the 99.9% bandwidth occupancy, among
the class of constant-to-low envelope variation pulses.
Index Terms Chip waveform optimization, direct-sequence
CDMA, envelope uniformity, multiple-access interference, phase
continuity.
I. I
NTRODUCTION
I
N THIS paper, we consider the performance of direct-
sequence code-division multiple-access (DS-CDMA) com-
munication systems with signaling schemes that use offset
linear quadrature modulation with arbitrary chip waveform
shapes, random signature sequences, and single-user cor-
relation receivers. Common examples of this category of
signaling schemes are offset quadrature phase-shift keying
(OQPSK) with the conventional rectangular chip waveform
Paper approved by U. Madhow, the Editor for Spread Spectrum of the
IEEE Communications Society. Manuscript received August 15, 1997; revised
September 15, 1998. This work was supported in part by the National Science
Foundation under Grant NCR-9115969.
M. A. Landolsi is with Nortel Networks, Wireless Solutions Division,
Ottawa, ON K1Y 4H7, Canada (e-mail: landolsi@nortelnetworks.com).
W. E. Stark is with the Department of Electrical Engineering and Com-
puter Science, University of Michigan, Ann Arbor, MI 48109 USA (e-mail:
stark@eecs.umich.edu).
Publisher Item Identier S 0090-6778(99)08915-1.
and minimum-shift keying (MSK) with the half-sine chip
waveform [1], [2].
It is well known that appropriate data pulse shaping in linear
quadrature modulation improves the spectral performance
of the modulation scheme because smooth signal transitions
yield a fast rolloff of the power spectrum of the signal and
improve its spectral connement. Such improved bandwidth
efciency is highly desirable in DS-CDMA applications
because it allows for the use of longer spreading codes at
a given allocated bandwidth, thereby improving the error
performance of the system for a given number of users or
making it possible to accommodate a larger number of users
for a given bit-error rate. In addition, for DS-CDMA systems
with a correlation receiver, pulse shaping by itself directly
impacts error performance. This is because the variance of
the multiple-access interference depends on the actual shape
of the chip waveform and not only on its energy [1]. This
is unlike communication over channels corrupted by additive
white Gaussian noise only, where pulses with different shapes
but with equal energy still have the same error performance.
There is comparatively little work done on the optimization
of chip waveforms for DS-CDMA systems. Instead, more
effort was devoted to the design of good spreading sequences
in order to better reduce interference and mitigate multipath
effects. This was also combined with the use of coding and
diversity schemes to further improve performance. Previous
results related to chip waveform design were presented in
[3] where suboptimum solutions to the problem of design-
ing pulses that achieve minimum squared correlation for a
given inband power were constructed based on the use of
prolate spheroidal wave functions [16]. For strictly band-
limited pulses (which therefore have innite time duration),
this problem was discussed in [18] and the optimal pulses
are found to have a constant spectrum, i.e., with a
shape in time-domain, as was also shown earlier in [3]. Chip
waveform optimization was similarly considered with binary
phase-shift keying (BPSK) modulation in [10], where direct
calculus of variation techniques were used to minimize the
multiple-access interference variance, but without considering
the additional gures of merit that we incorporate in this work
(namely, the bandwidth, phase, and envelope constraints, as
will be discussed shortly). Another problem involving pulse
shape design was considered in [11], where minimum rms
bandwidth is considered for a set of direct-sequence signals
with a specied correlation matrix. Also, optimal pulse shaping
00906778/99$10.00
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1999 IEEE 1738
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 11, NOVEMBER 1999
was considered in [12] for a different system model based on
orthogonal multicarrier quasi-synchronous CDMA. Additional
results that highlight the differences in performance (mainly
bit-error probability) between several known pulses can be
found in [8] and [13], and the importance of chip waveform
shaping in the mitigation of multipath effects in DS-CDMA
was also addressed in [14].
In this paper, following the work in [4] and [5], we consider
the case of full-response chip pulses, i.e., those limited to
a single chip interval and extend the design requirements
to solve for the optimal chip waveforms that achieve min-
imal multiple-access interference variance while preserving
several important signal features, including xed total signal
power, limited inband power bandwidth, phase continuity,
and envelope uniformity, which are necessary to preserve
the spectral performance of the signaling schemes, especially
when power-efcient nonlinear ampliers are used. The re-
sults obtained provide extensive performance comparisons and
benchmarking for several families of optimal chip waveforms
designed with various constraints and at different bandwidth
occupancy levels. In addition, the potential achievable gains
in performance of these optimal waveforms over some of
the conventional modulation schemes (e.g., OQPSK and other
MSK-type modulations) are also quantied. We also point out
that although our focus in this paper is limited to the family of
full-response pulse shapes, the optimization methodology used
is still applicable to the general case of partial-response pulses
with only a few modications to account for the different
signal format.
The rest of the paper is organized as follows. In Section II,
the system and signal models used are discussed. In
Section III, we formulate the optimization problem and
dene the various constraints. In Section IV, the solution
methodology is discussed based on the use of prolate
spheroidal wave functions. Several design examples and
numerical results are given in Section V, and nal conclusions
are presented in Section VI.
II. S
YSTEM
M
ODEL
We use the classical framework and notation of [1] and
[2], which focuses on the many-to-one system topology that
models the reverse (mobile-to-base) link of a single-cell DS-
CDMA system. We briey review this model here. Assuming
active users with transmitted signals of the generalized
OQPSK format, the information bits of user
are split into inphase and quadrature streams
(1)
(2)
where
is the unit pulse on the bit interval
, and the
data bits
and
are binary random variables
with equal probability. The data streams are multiplied by the
spectrum-spreading signals
(3)
(4)
where
and
are two distinct signature sequences
modeled as random, aperiodic, with independent, equally
likely chip symbols
. We assume
that each bit is coded with
chips (i.e.,
). The
chip waveform
is time-limite